Book ChapterDOI
Model Sets: A Survey
Reads0
Chats0
TLDR
Even when reduced to its simplest form, namely that of point sets in euclidean space, the phenomenon of genuine quasi-periodicity appears extraordinary as discussed by the authors Although it seems unfruitful to try and define the concept precisely, the following properties may be considered as representative.Abstract:
Even when reduced to its simplest form, namely that of point sets in euclidean space, the phenomenon of genuine quasi-periodicity appears extraordinary Although it seems unfruitful to try and define the concept precisely, the following properties may be considered as representative:
discreteness;
extensiveness;
finiteness of local complexity;
repetitivity;
diffractivity;
aperiodicity;
existence of exotic symmetry (optional)read more
Citations
More filters
Journal ArticleDOI
Weighted Dirac combs with pure point diffraction
Michael Baake,Robert V. Moody +1 more
TL;DR: In this article, a class of translation bounded complex measures, which have the form of weighted Dirac combs, on locally compact Abelian groups is investigated, and a sufficient set of conditions to ensure that the diffraction measure is a pure point measure is presented.
Journal ArticleDOI
Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra
Michael Baake,Daniel Lenz +1 more
TL;DR: In this paper, the authors consider topological dynamical systems arising from locally compact Abelian groups on compact spaces of translation bounded measures and show that such a system has a pure point dynamical spectrum if and only if its diffraction spectrum is pure point.
Journal ArticleDOI
Characterization of model sets by dynamical systems
TL;DR: In this paper, it is shown how regular model sets can be characterized in terms of the regularity properties of their associated dynamical systems, and that regular models are as close to periodic sets as possible among repetitive aperiodic sets.
Journal ArticleDOI
Characterizations of model sets by dynamical systems
TL;DR: In this article, it is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems, and that regular models are as close to periodic sets as possible among repetitive aperiodic sets.
Posted Content
Weighted Dirac combs with pure point diffraction
Michael Baake,Robert V. Moody +1 more
TL;DR: In this article, a class of translation bounded complex measures, which have the form of weighted Dirac combs, on locally compact Abelian groups is investigated, and a sufficient set of conditions to ensure that the diffraction measure is a pure point measure is presented.
References
More filters
Book
Sphere packings, lattices, and groups
TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Journal ArticleDOI
Tilings and patterns
TL;DR: In this paper, the authors present a comprehensive reference on tiling theory for many decades, bringing together older results that have not been brought together before, and containing a wealth of new material.
Book
Recurrence in Ergodic Theory and Combinatorial Number Theory
TL;DR: The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press, to preserve the original texts of these important books while presenting them in durable paperback editions.
Posted Content
Sphere packings I
TL;DR: A program to prove the Kepler conjecture on sphere packings is described and it is shown that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture.
Journal ArticleDOI
Über die Gleichverteilung von Zahlen mod. Eins
TL;DR: In this article, the authors present a Gebrauch bestimmt ausschließlich für den persönlichen, nicht kommerziellen Gebrauchs, which is a rechtschutzbestimmter gebrauch, and gilt vorbehaltlich der folgenden Einschränkungen.